Finite Group Databasebeta

C2×#13130663 #16797752

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13130663

Splittings

FittingC23×D4×C13 ⋊ C4
SylowC13 ⋊ C2×#1781

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC23×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×D13C2
cosocleC23×D13C24
hypercenterC23×D4#261
hypocenterC13C2×#1781
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C23×D4

6254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104401);